The hosts had the points wrapped up by half-time thanks to goals from Jozy Altidore, Rasmus Elm (penalty) and Adam Maher, and Brett Holman put the icing on the cake with the fourth goal four minutes into the second half.
Daniel Larsson got Malmo on the scoresheet with a 72nd-minute penalty but it was too little too late to affect the outcome.
The Swedish visitors had a couple of early sights of goal, Math Ranegie firing wide and Jimmy Durmaz's 20-yard attempt easily dealt with by AZ goalkeeper Esteban Alvarado.
But they could not find the breakthrough and AZ showed them how it was done in the 21st minute when United States forward Altidore lashed a fierce strike into the top-right corner from 30 yards.
Malmo sought an immediate equaliser but Alvarado was never unduly troubled.
Larsson mis-hit his left-footed shot over the bar and the AZ stopper was more than equal to a left-footed free-kick from Ricardinho.
Ricardinho was involved at the other end soon after when he brought down Roy Beerens to hand AZ the opportunity to go two goals to the good. Elm stepped up to blast the spot-kick into the top-right corner.
Any hopes Malmo may have harboured of mounting a comeback were extinguished in the 39th minute when Maher unleashed a right-footed volley high past a helpless Johan Dahlin.
Dahlin was on hand to keep out a Holman shot soon after the restart but was powerless to prevent the same player extending the margin in the 49th minute, the Australia winger slotting into the bottom-right corner from 12 yards.
Wilton Figueiredo sent a couple of shots harmlessly wide as Malmo searched for a consolation goal. It arrived 18 minutes from time when Larsson despatched a penalty into the top-left corner after he had been fouled by Etienne Reijnen.
The visitors could have reduced the deficit further when Alvarado fumbled a Jiloan Hamad blast in the 82nd minute, but no Malmo player was able to capitalise, while three minutes later the AZ keeper made a fine save to keep out Ulrich Vinzents' drive from the edge of the box.
Johann Berg Gudmundsson also tried his luck from distance for AZ with a left-footed effort which fizzed just wide.
There were to be no further goals, but AZ had already done more than enough.